Adaptive high pressure fuel pump system and method for predicting pumped mass

ABSTRACT

A method of adaptively predicting, during operation of a pump, a mass of fuel pumped by the pump during a pumping event to a fuel accumulator (“Q pump ”) to control operation of the pump is provided, comprising: generating an adaptive model of operation of the pump, including estimating a start of pumping (“SOP”) position of a plunger of the pump, estimating Q pump , determining a converged value of the estimated SOP position, and determining a converged value of the estimated Q pump ; using the adaptive model to predict Q pump  by inputting to the model the converged value of the estimated SOP position, a measured pressure of fuel in the fuel accumulator and a measured temperature of fuel in the fuel accumulator; and controlling operation of the pump in response to the predicted Q pump .

RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 17/046,887, entitled “ADAPTIVE HIGH PRESSURE FUEL PUMP SYSTEMAND METHOD FOR PREDICTING PUMPED MASS,” filed on Oct. 12, 2020, which isa national phase filing of PCT Application S/N PCT/US2018/026891, filedon Apr. 10, 2018, the entire disclosures of which being expresslyincorporated herein by reference.

TECHNICAL FIELD

The present invention relates generally to fuel pumps and moreparticularly to methods and systems for adaptively modeling theoperation of high pressure fuel pumps to predict pumped fuel mass forcontrol and diagnostic applications.

BACKGROUND

In internal combustion engines, one or more fuel pumps deliver fuel to afuel accumulator. Fuel is delivered by fuel injectors from theaccumulator to cylinders of the engine for combustion to power operationof the system driven by the engine. It is desirable for a variety ofreasons to accurately characterize the amount of fuel delivered by thefuel pump to the accumulator. In conventional fuel delivery systems,operation of the fuel pump is characterized periodically by shuttingdown the fuel pump and measuring various variables of the fuel deliverysystem. Such an approach is disruptive to the operation of the engineand provides inaccurate results. As such, an improved approach topredicting the amount of fuel pumped by the fuel pump during operationof the pump is needed.

SUMMARY

According to one embodiment, the present disclosure provides a method ofadaptively predicting, during operation of a pump, a mass of fuel pumpedby the pump during a pumping event to a fuel accumulator (“Q_(pump)”) tocontrol operation of the pump, comprising: generating an adaptive modelof operation of the pump, including estimating a start of pumping(“SOP”) position of a plunger of the pump, estimating Q_(pump),determining a converged value of the estimated SOP position, anddetermining a converged value of the estimated Q_(pump); using theadaptive model to predict Q_(pump) by inputting to the model theconverged value of the estimated SOP position, a measured pressure offuel in the fuel accumulator and a measured temperature of fuel in thefuel accumulator; and controlling operation of the pump in response tothe predicted Q_(pump). In one aspect of this embodiment, estimating aSOP position includes: receiving raw measurements of pressure of fuel inthe fuel accumulator; identifying quiet segments in the rawmeasurements; fitting a model to the identified quiet segments; usingthe fitted model to determine an output representing a propagation ofthe pressure of fuel in the fuel accumulator without disturbance frompumping events; and identifying a divergence between the fitted modeloutput and the raw measurements of pressure of fuel in the fuelaccumulator. In a variant of this aspect, identifying quiet segmentsincludes filtering the raw measurements with a median filter having alength corresponding to a frequency of oscillation of the pressure offuel in the fuel accumulator. In a further variant, the median filter istuned to the frequency of oscillation, a sonic speed of the fuel and ageometry of the fuel accumulator. In still a further variant,identifying quiet segments further includes evaluating a derivative ofthe filtered raw measurements to identify segments of the derivativehaving approximately zero slope. In another variant, fitting a model tothe identified quiet segments includes using the relationship P=Pmean+

sin(ω₁t+φ₁)+

sin(ω₂t+φ₂). In another aspect of this

embodiment, estimating Q_(pump) includes calculating a pressuredifference between a mean pressure before a pumping event and a meanpressure after a pumping event. In a variant of this aspect, estimatingQ_(pump) further includes converting the calculated pressure differenceinto mass. In another aspect, the adaptive model uses the relationshipQpump=fcam(EOP−SOP)*A*δ(P,T)−t*L(P,T), wherein fcam is a tablecorrelating positions of the plunger to a crank angle of an engine, EOPis an end of pumping position of the plunger, A is an area of theplunger, δ(P,T) is a density of fuel in the fuel accumulator, t is aduration of the pumping event, and L(P,T) is a leakage of fuel from thepump. In a variant of this aspect, δ(P,T) is modeled by either a firstorder polynomial in a fuel temperature dimension or at least a secondorder polynomial in a fuel pressure dimension. In another variant,L(P,T) is modeled by either a first order polynomial in a fueltemperature dimension or at least a second order polynomial in a fuelpressure dimension. In another aspect, controlling operation of the pumpincludes adjusting one of a timing of the pumping event or a duration ofthe pumping event.

In another embodiment of the present disclosure, a system is providedfor adaptively predicting, during operation of a pump, a mass of fuelpumped by the pump during a pumping event to a fuel accumulator(“Q_(pump)”) to control operation of the pump, comprising: a pressuresensor positioned to measure pressure of fuel in the fuel accumulator; atemperature sensor positioned to measure temperature of fuel in the fuelaccumulator; and a processor in communication with the pressure sensorto receive pressure values representing the measured pressure of thefuel in the fuel accumulator and in communication with the temperaturesensor to receive temperature values representing the measuredtemperature of the fuel in the fuel accumulator; wherein the processoris configured to generate an adaptive model of operation of the pump byestimating a start of pumping (“SOP”) position of a plunger of the pump,estimating Q_(pump), determining a converged value of the estimated SOPposition, and determining a converged value of the estimated(“Q_(pump)”), use the adaptive model to predict (“Q_(pump)”) byinputting to the model the converged value of the estimated SOPposition, a pressure value and a temperature value, and controloperation of the pump in response to the predicted (“Q_(pump)”). In oneaspect of this embodiment, the processor is configured to estimate a SOPposition includes by receiving the pressure values, identifying quietsegments in the pressure values, fitting a model to the identified quietsegments, using the fitted model to determine an output representing apropagation of the pressure of fuel in the fuel accumulator withoutdisturbance from pumping events, and identifying a divergence betweenthe fitted model output and the pressure values. In a variant of thisaspect, the processor is configured to identify the quiet segments byfiltering the pressure signals with a median filter having a lengthcorresponding to a frequency of oscillation of the pressure of fuel inthe fuel accumulator. In another variant, the processor is configured toidentify the quiet segments by evaluating a derivative of the filteredpressure signals to identify segments of the derivative havingapproximately zero slope. In another aspect, the processor is configuredto estimate Q_(pump) by calculating a pressure difference between a meanpressure before a pumping event and a mean pressure after a pumpingevent. In still another aspect, the adaptive model uses the relationshipQpump=fcam(EOP−SOP)*A*δ(P,T)−t*L(P,T), wherein fcam is a tablecorrelating positions of the plunger to crank angle of an engine, EOP isan end of pumping position of the plunger, A is an area of the plunger,δ(P,T) is a density of fuel in the fuel accumulator, t is a duration ofthe pumping event, and L(P,T) is a leakage of fuel from the pump. In avariant of this aspect, at least one of δ(P,T) and L(P,T) is modeled byeither a first order polynomial in a fuel temperature dimension or atleast a second order polynomial in a fuel pressure dimension. In yetanother aspect, the processor is configured to control operation of thepump by adjusting one of a timing of the pumping event or a duration ofthe pumping event.

While multiple embodiments are disclosed, still other embodiments of thepresent invention will become apparent to those skilled in the art fromthe following detailed description, which shows and describesillustrative embodiments of the invention. Accordingly, the drawings anddetailed description are to be regarded as illustrative in nature andnot restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

The above-mentioned and other features of this disclosure and the mannerof obtaining them will become more apparent and the disclosure itselfwill be better understood by reference to the following description ofembodiments of the present disclosure taken in conjunction with theaccompanying drawings, wherein:

FIG. 1 is a schematic diagram of a fueling system;

FIG. 2 is a graph showing measured rail pressure and a median filteredrepresentation of the measured rail pressure;

FIG. 3 is a graph similar to FIG. 2 showing quiet segments of themeasured rail pressure;

FIG. 4 is a graph similar to FIG. 3 showing an output trace of a modelaccording to the present disclosure;

FIG. 5 is a graph similar to FIG. 4 showing an estimated start ofpumping position for a fuel pump;

FIG. 6 is a graph of the difference between the measured rail pressureof FIG. 4 and the output trace of FIG. 4; and

FIG. 7 is a graph showing the mean rail pressure before and after apumping event.

While the present disclosure is amenable to various modifications andalternative forms, specific embodiments have been shown by way ofexample in the drawings and are described in detail below. The presentdisclosure, however, is not to limit the particular embodimentsdescribed. On the contrary, the present disclosure is intended to coverall modifications, equivalents, and alternatives falling within thescope of the appended claims.

DETAILED DESCRIPTION

One of ordinary skill in the art will realize that the embodimentsprovided can be implemented in hardware, software, firmware, and/or acombination thereof. For example, the controllers disclosed herein mayform a portion of a processing subsystem including one or more computingdevices having memory, processing, and communication hardware. Thecontrollers may be a single device or a distributed device, and thefunctions of the controllers may be performed by hardware and/or ascomputer instructions on a non-transient computer readable storagemedium. For example, the computer instructions or programming code inthe controller (e.g., an electronic control module (“ECM”)) may beimplemented in any viable programming language such as C, C++, HTML,XTML, JAVA or any other viable high-level programming language, or acombination of a high-level programming language and a lower levelprogramming language.

As used herein, the modifier “about” used in connection with a quantityis inclusive of the stated value and has the meaning dictated by thecontext (for example, it includes at least the degree of errorassociated with the measurement of the particular quantity). When usedin the context of a range, the modifier “about” should also beconsidered as disclosing the range defined by the absolute values of thetwo endpoints. For example, the range “from about 2 to about 4” alsodiscloses the range “from 2 to 4.”

Referring now to FIG. 1, a schematic diagram of a portion of a highpressure pump is shown. Pump 10 includes a plunger 12 that reciprocateswithin a barrel 14 as is known in the art. Fuel is supplied to a chamber16 within barrel 14 through an inlet 18, compressed by upward motion ofplunger 12 such that the pressure of the fuel is increased, and suppliedthrough an outlet 20 to an outlet check valve (OCV) 22 and to a fuelreservoir, such as a common rail accumulator (hereinafter, rail 24).Fuel from rail 24 is periodically delivered by a plurality of fuelinjectors 25 to a corresponding plurality of cylinders (not shown) of aninternal combustion engine (not shown). A small circumferential gap 26exists between an outer surface 28 of plunger 12 and an inner surface 30of barrel 14 to permit reciprocal motion of plunger 12 within barrel 14.

As plunger 12 moves through the pumping cycle, it moves between astart-of-pumping (SOP) position and an end-of-pumping (EOP) position.The SOP position is after plunger 12 moves through itsbottom-dead-center (BDC) position and the EOP position precedes thetop-dead-center (TDC) position of plunger 12.

As indicated above, during the compression stroke of plunger 12 (i.e.,as it moves from the BDC position to the TDC position), fuel in chamber16 is compressed, causing the pressure in chamber 16 to increase to apoint where the force on the chamber side of OCV 22 is equal to theforce on the rail side of OCV 22. As a result, OCV 22 opens and fuelbegins to flow through outlet 20 and OCV 22 to rail 24. Fuel continuesto flow in this manner to rail 24 as plunger 12 continues to traveltoward the TDC position. Consequently, the pressure of fuel in rail 24increases. A processor 21 receives measurements of the pressure of fuelwithin rail 24 from a pressure sensor 23 and the temperature of fuelwithin rail 24 from a temperature sensor 27. Processor 21 also controlsoperation of injectors 25 as described herein.

The present disclosure provides a model of high pressure pump 10 that isuseful for, among other things, predicting the mass of fuel pumped bypump 10 to rail 24, a prediction that provides benefits for fuel controlsystems as described herein. For purposes of the model, it is assumedthat during the pumping operation of pump 10, fuel can only flow assupply fuel through outlet 20 and OCV 22 to rail 24 and/or as leakagethrough gap 26 to a return line 32 (which routes the fuel back to a fueltank (not shown)). This characteristic of pump 10 may be describedmathematically by the following equation:

Qpump=fcam(EOP−SOP)*A*δ(P,T)−t*L(P,T)  (1)

where Qpump is the outputted mass to rail 24 by pump 10, fcam is apolynomial or table describing the relationship between the crank angle(in degrees) and the lift of plunger 12. More specifically, as pump 10is coupled to the engine crankshaft through a gear assembly and isdriven in operation by rotation of the crankshaft, the crank angle ofthe crankshaft is directly related to the position of plunger 12 of pump10. As such, the location of SOP and EOP may be expressed in terms ofcrank angle. Once the SOP is determined, the swept height of plunger 12(and therefore the swept volume of chamber 16) during a pumping cyclemay be determined, given knowledge of the geometry of pump 10. The tablerepresented by fcam may be a look-up table that is specific to aparticular pump 10 and correlates crank angle to the position of plunger12. [00022] (EOP-SOP) describes the number of crank angle degreesbetween the SOP position and EOP position. The difference between theTDC position and the EOP position should be understood. The TDC positionis when plunger 12 physically reaches its top position, while the EOPposition is the end of the pumping stroke as observed by pressure sensor23. As is understood by those skilled in the art, the relationshipbetween the TDC position and the EOP position depends on the sonic speedof the fuel and the geometry of the high pressure system (i.e., rail24).

With further reference to Equation (1) above, A is the area of plunger12. The area A together with fcam(EOP-SOP) determines the swept volumeof fuel pumped to rail 24. δ(P,T) is the density of the fuel, which canbe modeled as a first order polynomial in the T (fuel temperature)dimension and a second order polynomial in the P (pressure is rail 24)dimension. The duration of the pumping stroke while OCV 22 is opened isrepresented by t (time). Finally, L(P,T) represents the fuel leakage(i.e., between barrel 14 and plunger 12), and can be described as afirst order polynomial in the T dimension and a higher order polynomialin the P dimension. In certain embodiments, P^(2.5) may be used. Itshould be understood that cross terms between the temperature andpressure are likely.

Given the SOP position of plunger 12 (the determination of which isdescribed below), pressure from pressure sensor 23 and temperature fromtemperature sensor 27, the model can be used to predict the outputtedmass of pump 10 under any set of operating conditions. While useful, theabove-described model relies on known values for leakage, fuel densityand the EOP position. Unfortunately, leakage varies with part-to-partvariations (e.g., plunger 12 and barrel 14) and wear of the parts overtime. Fuel density is different for different types and sources of fuel.Additionally, the EOP position is usually not known for a particularpump 10 on a particular engine. According to the principles of thepresent disclosure, the pump model may be made adaptive by estimatingthe unknown variables using an Extended Kalman filter.

As indicated above, rail pressure sensor 23 and rail temperature sensor27 provide measurements of the pressure of fuel in rail 24 and thetemperature of fuel in rail 24, respectively, to processor 21. Inaddition to these inputs, the above-mentioned adaptive pump modelrequires estimates for the SOP position and Qpump. As indicated above,the SOP position may be indicated by the time of occurrence of anincrease in a trace of the pressure of fuel in rail 24 (i.e., railpressure) due to the pumping operation of pump 10. To identify the SOPposition in this manner, quiet segments in a buffer of rail pressuremeasurements may first be determined. These quiet segments correspond tothe absence of pumping fuel into or injecting fuel from rail 24. Thequiet segments may be determined by processing rail pressuremeasurements with a median filter with a length corresponding to theperiod of time of the mode of operation of rail 24. The mode ofoperation corresponds to the frequency or frequencies of oscillation ofpressure within rail 24. There may be one or more sinusoidal modes whichare accounted for by the median filter to remove the oscillations andidentify when pumping and quiet segments occur. If multiple frequenciesof oscillation exist, then the median filter is run multiple times withdifferent filter lengths corresponding to the different frequencies.

Referring now to FIG. 2, raw rail pressure is shown as trace 34 and themedian filtered version of trace 34 is depicted as trace 36. As shown bytrace 36, the median filter effectively removes noise and oscillationsfrom trace 34 while maintaining the injection and pumpingcharacteristics of the raw data without losing any important highfrequency information. The filter is similar to a centered movingaverage, but uses median pressure instead of average pressure. Thefilter is tuned to the frequency of oscillation predicted for aparticular rail pressure, sonic speed of the fuel and geometry of rail24.

Referring now to FIG. 3, processor 21 may identify quiet segments fromthe output of the median filter by evaluating the derivative of trace 36(i.e., the filtered rail pressure signal). The quiet segments arehighlighted as segments 38 in FIG. 3. It should be understood that quietsegments 38 are simply those portions of raw data trace 34 thatcorrespond to horizontal or flat portions of filtered data trace 36. Inother words, quite segments of raw data trace 34 correspond in time tosegments of filtered data trace 36 having approximately zero slope.

According to the present disclosure, processor 21 next fits a 2-modemodel to the identified quiet segments 38. The model is described byEquation (2) below.

P=Pmean+

sin(ω₁ t+φ ₁)+

sin(ω₂ t+φ ₂)  (2)

where it is assumed that damping factors

and angular velocities ω_(i) (both of which depend on sonic speed) areknown. As should be understood by those skilled in the art with thebenefit of the present disclosure, equation (2) may be modified toinclude any number of modes by including additional sinusoidal terms.Equation (2) can be rewritten using trigonometric relationships asfollows:

P=Pmean+

sin(ω₁ t)cos(φ₁)+

cos(ω₁ t)sin(φ₁)+

sin(ω₂ t)cos (φ₂)+

cos(ω₂ t)sin(φ₂)  (3)

Equation (3) can be further rewritten as a linear system which may beused by processor 21 to obtain a least squares estimate of Pmean,a₁*cos(φ₁), a₂*cos(φ₂), a₁*sin(φ₁) and a₂*sin(φ₂). Values for a_(i) andφ_(i) can be found by solving the linear system

$\quad\{ \begin{matrix}{a_{i}*} & {{\cos( \varphi_{i} )} = x_{1}^{i}} \\{a_{i}*} & {{\sin( \varphi_{i} )} = x_{2}^{i}}\end{matrix} $

which has the solutions

$\varphi_{i} = {{acos}( \frac{x_{1}^{i}}{\sqrt{x_{1}^{i^{2}} + x_{2}^{i^{2}}}} )}$${a\; 1} = \sqrt{x_{1}^{i^{2}} + x_{2}^{i^{2}}}$

As such, the amplitude, phase, damping and frequency of the freeresponse dynamics are known, and the propagation of the rail pressuredynamics may be represented without the disturbance of pumping events.The output of this model is plotted as trace 40 in FIG. 4 along with thedata on which it is based.

In the next step, the difference between the raw rail pressure data(trace 34) and the model (trace 40) can be used by processor 21 toobtain an estimation of the SOP position. Referring to FIG. 5, theestimated SOP position is indicated as dot 42. The estimated SOPposition 42 is where the raw data and the fitted model diverge from oneanother. FIG. 6 shows the difference between the raw rail pressure data(trace 34) and the fitted model (trace 40).

The fuel mass transferred from pump 10 to rail 24 (i.e., Q_(pump)) maybe estimated in a manner similar to conventional estimations of fuelinjection quantities. AP is measured by pressure sensor 23, read byprocessor 21, and then converted to mass using knowledge of thepressurized volume and the sonic speed in the fuel. AP is calculated byprocessor 21 as the difference between the mean pressure before andafter a pumping event as depicted in FIG. 7. The mean pressures areobtained using the same least squares procedure used to obtain anestimate for the SOP position (described above), where the mean pressurewas one of the estimated values.

After the adaptive pump model described above converges, the pumped massmay be predicted by feeding the model with the SOP position, railpressure and rail temperature. Using the model of the presentdisclosure, fuel injection measurements may be obtained withoutdeactivating high pressure pump 10. Further details of this applicationof the model according to the present disclosure are described inco-pending patent application S/N PCT/US2018/026874, entitled “SYSTEMAND METHOD FOR MEASURING FUEL INJECTION DURING PUMP OPERATION,” filed onApr. 10, 2018 (hereinafter, “the Injection Measuring Application”), theentire disclosure of which being expressly incorporated herein byreference. In this sense the present disclosure provides a non-intrusivemeasurement method as data is gathered during normal operation. Also,the present model may be used to estimate fuel density, which can beused to determine the type of fuel (diesel, winter diesel, biodiesel,etc.) being pumped by pump 10. Additionally, the present model may beused in a feed-forward application to provide better control over thefuel pressure in rail 24. When injectors 25 inject fuel from rail 24,the fuel in rail 24 needs to be replaced to maintain mass balance in thesystem. As such, the timing and extent to which pump 10 is operated canbe controlled according to the principles of the present disclosure tomaintain mass balance as determined by the adaptive model describedherein. Moreover, the model may be used to monitor fuel injectionquantities, pump output, and/or leakage for diagnostic purposes.

It should be understood that the teachings of the present disclosureprovide a mechanism for understanding the performance of pump 10 (e.g.,the extent to which it leaks, etc.). In the Injection MeasuringApplication, the pump performance determined by the present applicationis used to determine the quantity of fuel injected by each fuelinjection event, and that is used to control the fuel injectors andperform diagnostics.

Additionally, the adaptive model of the present disclosure permitscomputation of fuel efficiency (e.g., miles per gallon) because fueldensity, injection quantities and leakage can be estimated. Moreover, asthe EOP may be identified, the synchronization or timing of the pumpingevents relative to the fuel injection events may be determined. Thisinformation may be used to control the characteristics of the pumpingevents (timing and/or duration), determine if the pump was installedincorrectly, and adjust the operation of the pump to increase itsoperational life.

It should be understood that, the connecting lines shown in the variousfigures contained herein are intended to represent exemplary functionalrelationships and/or physical couplings between the various elements. Itshould be noted that many alternative or additional functionalrelationships or physical connections may be present in a practicalsystem. However, the benefits, advantages, solutions to problems, andany elements that may cause any benefit, advantage, or solution to occuror become more pronounced are not to be construed as critical, required,or essential features or elements. The scope is accordingly to belimited by nothing other than the appended claims, in which reference toan element in the singular is not intended to mean “one and only one”unless explicitly so stated, but rather “one or more.” Moreover, where aphrase similar to “at least one of A, B, or C” is used in the claims, itis intended that the phrase be interpreted to mean that A alone may bepresent in an embodiment, B alone may be present in an embodiment, Calone may be present in an embodiment, or that any combination of theelements A, B or C may be present in a single embodiment; for example, Aand B, A and C, B and C, or A and B and C.

In the detailed description herein, references to “one embodiment,” “anembodiment,” “an example embodiment,” etc., indicate that the embodimentdescribed may include a particular feature, structure, orcharacteristic, but every embodiment may not necessarily include theparticular feature, structure, or characteristic. Moreover, such phrasesare not necessarily referring to the same embodiment. Further, when aparticular feature, structure, or characteristic is described inconnection with an embodiment, it is submitted that it is within theknowledge of one skilled in the art with the benefit of the presentdisclosure to affect such feature, structure, or characteristic inconnection with other embodiments whether or not explicitly described.After reading the description, it will be apparent to one skilled in therelevant art(s) how to implement the disclosure in alternativeembodiments.

Furthermore, no element, component, or method step in the presentdisclosure is intended to be dedicated to the public regardless ofwhether the element, component, or method step is explicitly recited inthe claims. No claim element herein is to be construed under theprovisions of 35 U.S.C. 112(f), unless the element is expressly recitedusing the phrase “means for.” As used herein, the terms “comprises,”“comprising,” or any other variation thereof, are intended to cover anon-exclusive inclusion, such that a process, method, article, orapparatus that comprises a list of elements does not include only thoseelements but may include other elements not expressly listed or inherentto such process, method, article, or apparatus

Various modifications and additions can be made to the exemplaryembodiments discussed without departing from the scope of the presentdisclosure. For example, while the embodiments described above refer toparticular features, the scope of this disclosure also includesembodiments having different combinations of features and embodimentsthat do not include all of the described features. Accordingly, thescope of the present disclosure is intended to embrace all suchalternatives, modifications, and variations as fall within the scope ofthe claims, together with all equivalents thereof.

We claim:
 1. A method of predicting a mass of fuel pumped by a pumpduring a pumping event to a fuel accumulator (“Q_(pump)”) to controloperation of the pump, comprising: generating a model of operation ofthe pump, including determining a converged value of an estimated startof pumping (“SOP”) position of a plunger of the pump; using the model topredict Q_(pump) by inputting to the model the converged value of theestimated SOP position, a measured pressure of fuel in the fuelaccumulator and a measured temperature of fuel in the fuel accumulator;and controlling operation of the pump in response to the predictedQ_(pump).
 2. The method of claim 1, further comprising estimating a SOPposition by: receiving raw measurements of pressure of fuel in the fuelaccumulator; identifying quiet segments in the raw measurements; fittinga model to the identified quiet segments; using the fitted model todetermine an output representing a propagation of the pressure of fuelin the fuel accumulator without disturbance from pumping events; andidentifying a divergence between the fitted model output and the rawmeasurements of pressure of fuel in the fuel accumulator.
 3. The methodof claim 2, wherein identifying quiet segments includes filtering theraw measurements with a median filter having a length corresponding to afrequency of oscillation of the pressure of fuel in the fuelaccumulator.
 4. The method of claim 3, wherein the median filter istuned to the frequency of oscillation, a sonic speed of the fuel and ageometry of the fuel accumulator.
 5. The method of claim 3, whereinidentifying quiet segments further includes evaluating a derivative ofthe filtered raw measurements to identify segments of the derivativehaving approximately zero slope.
 6. The method of claim 2, whereinfitting a model to the identified quiet segments includes using therelationship P=Pmean+

sin(ω₁t+φ₁)+

sin(ω₂t+φ₂).
 7. The method of claim 1, further comprising estimatingQ_(pump) by calculating a pressure difference between a mean pressurebefore a pumping event and a mean pressure after a pumping event.
 8. Themethod of claim 7, wherein estimating Q_(pump) further includesconverting the calculated pressure difference into mass.
 9. The methodof claim 1, wherein the model uses the relationshipQpump=fcam(EOP−SOP)*A*δ(P,T)−t*L(P,T), wherein fcam is a tablecorrelating positions of the plunger to a crank angle of an engine, EOPis an end of pumping position of the plunger, A is an area of theplunger, δ(P,T) is a density of fuel in the fuel accumulator, t is aduration of the pumping event, and L(P,T) is a leakage of fuel from thepump.
 10. The method of claim 9, wherein δ(P,T) is modeled by either afirst order polynomial in a fuel temperature dimension or at least asecond order polynomial in a fuel pressure dimension.
 11. The method ofclaim 9, wherein L(P,T) is modeled by either a first order polynomial ina fuel temperature dimension or at least a second order polynomial in afuel pressure dimension.
 12. The method of claim 1, wherein controllingoperation of the pump includes adjusting one of a timing of the pumpingevent or a duration of the pumping event.
 13. A system for predicting amass of fuel pumped by a pump during a pumping event to a fuelaccumulator (“Q_(pump)”) to control operation of the pump, comprising: apressure sensor positioned to measure pressure of fuel in the fuelaccumulator; a temperature sensor positioned to measure temperature offuel in the fuel accumulator; and a processor in communication with thepressure sensor to receive pressure values representing the measuredpressure of the fuel in the fuel accumulator and in communication withthe temperature sensor to receive temperature values representing themeasured temperature of the fuel in the fuel accumulator; wherein theprocessor is configured to generate a model of operation of the pump bydetermining a converged value of an estimated start of pumping (“SOP”)position of a plunger of the pump, use the model to predict (“Q_(pump)”)by inputting to the model the converged value of the estimated SOPposition, a pressure value and a temperature value, and controloperation of the pump in response to the predicted (“Q_(pump)”).
 14. Thesystem of claim 13, wherein the processor is configured to estimate aSOP position by receiving the pressure values, identifying quietsegments in the pressure values, fitting a model to the identified quietsegments, using the fitted model to determine an output representing apropagation of the pressure of fuel in the fuel accumulator withoutdisturbance from pumping events, and identifying a divergence betweenthe fitted model output and the pressure values.
 15. The system of claim14, wherein the processor is configured to identify the quiet segmentsby filtering the pressure signals with a median filter having a lengthcorresponding to a frequency of oscillation of the pressure of fuel inthe fuel accumulator.
 16. The system of claim 15, wherein the processoris configured to identify the quiet segments by evaluating a derivativeof the filtered pressure signals to identify segments of the derivativehaving approximately zero slope.
 17. The system of claim 13, wherein theprocessor is configured to estimate Q_(pump) by calculating a pressuredifference between a mean pressure before a pumping event and a meanpressure after a pumping event.
 18. The system of claim 13, wherein themodel uses the relationship Qpump=fcam(EOP−SOP)*A*δ(P,T)−t*L(P,T),wherein fcam is a table correlating positions of the plunger to crankangle of an engine, EOP is an end of pumping position of the plunger, Ais an area of the plunger, δ(P,T) is a density of fuel in the fuelaccumulator, t is a duration of the pumping event, and L(P,T) is aleakage of fuel from the pump.
 19. The system of claim 18, wherein atleast one of δ(P,T) and L(P,T) is modeled by either a first orderpolynomial in a fuel temperature dimension or at least a second orderpolynomial in a fuel pressure dimension.
 20. The system of claim 13,wherein the processor is configured to control operation of the pump byadjusting one of a timing of the pumping event or a duration of thepumping event.